How Does Competition Affect Productivity in New Zealand?

Honours Research Meeting

Benjamin Stubbing

September 4, 2025

What I’m doing, why it matters & what I’ll talk about today

Productivity is one of the biggest long-run determinants of living standards: NZ faces a secular productivity challenge, so it’s valuable to learn how much of the variance in productivity is attributable to (lack of) competition
Previous work was limited by data variation and analysis was associative
I’m using a longer time series and trying to identify causal inference

No results to summarise at this point; instead, I’m going to talk about:

data prep: how I used the LBD to measure competition and productivity
methods & where identification is coming from

1. Data Prep

To estimate competition’s productivity effects, we need variables for competition and productivity

Using the Longitudinal Business Database (LBD), which provides administrative firm-level data…

Competition is estimated by Herfindahl-Hirshman index
Productivity is estimated by Total Factor Productivity (TFP)

We measure productivity as TFP: that which is not explained by observables

\[\text{Gross Output} = f(\text{Capital}, \text{Labour}, \text{Intermediates}) \times \text{TFP}\]

Intuition: TFP is efficiency in turning inputs into outputs
TFP \(=\) firm FE + time-varying residual
- Fixed effects absorb industry-year shocks and capture persistent firm productivity
N.b., revenue-based TFP \(\neq\) pure technology, it also reflects demand & markup shocks (Klette–Griliches critique)

To get TFP, we create production functions using LBD admin data

Data-prep

2. Methods & Identification

Why is competition associated with productivity?

1. Treatment Effect

Competition directly affect on productivity, induceing firms to adopt some characteristics commensurate with productivity (e.g., R&D, managerial talent)

2. Selection Effect

Competition leads to selective attrition of low-productivity firms: More-efficient firms accumulate market share, forcing the exit of less-efficient firms

To disentangle the two effects, I’m adapting 2 methods from Backus¹:

Olley-Pakes decomposition
Quantile-regression

How do we identify competition’s productivity effects?

Source of endogeneity	Mitigation
Reverse causality (simultaneity)	IV: demand shifters (strong first stage)
Omitted variables	Firm FE + market trends; IV (demand/policy shocks)
Measurement confounds (TFPR)	Careful deflators; note TFPR ≠ pure technology

A demand shifter is a factor that predicts consumer demand without directly changing firms’ production technology
Relevance: demand shifter \(\implies\) market size/composition \(\rightarrow\) entry/exit & share reallocation \(\rightarrow\) HHI moves mechanically
Validity: After deflation and FE, demand shifter affects TFPR only via competition

Even with PPI-Outputs/Inputs and CGPI deflation, deflated TFPR still embeds markup/utilization. Our exclusion is conditional: \(Z\) must not move these residual components except via competition. We therefore interpret \(\beta\) as the effect of competition on deflated TFPR, not pure TFPQ.

Relevance is mechanical: demand shifters change demand \(\rightarrow\) who competes \(\rightarrow\) HHI
Validity is conditional on our controls/deflators; we’re transparent that TFPR ≠ technology
Interpretation: effect on deflated TFPR; I’m testing whether this is credible

Bias intuition

Reverse causality: productivity shocks raise HHI (big firms expand, entrants deterred). Biases estimates upward.
Omitted variables: local shocks (infrastructure, policy) hit both productivity & competition. Sign ambiguous.
Measurement confounds: with revenue-based TFP, higher HHI → higher markups → higher measured TFPR even if no tech gain (Klette–Griliches).

Why the first stage should be strong* (one liner): Demand shifters pass through to P,Q with elastic entry/share realocation, HHI moves a lot

Credibility checks we can report

Strength and monotonicity: first stage F
Placebo/pre-trend: does demand shock predict pre-period TFPR trends once FE included?
Price/markup procies: conditional on competition, demand shifter has little residual power for firm-level prices/markups
Market definition sensitivity

Did the Good Firms Get Bigger, or Did the Average Firm Just Get Less Bad (or Die)?

Olley-Pakes decomposition splits market-level productivity into unweighted mean & covariance term that captures reallocation across survivors:

If market shares reshuffle toward high-TFP among survivors \(\rightarrow\) intensive (OP covariance)
If the set of plants itself improve \(\rightarrow\) extensive (unweighted mean), but could move for two reasons:
1. within-plant treatment
2. selection (because the cross-section you average over changed)

OP shows us upon which margin competition affects productivity, but within the mean it cannot separate treatment from selection

Does Competition Kill Losers or Make Everyone Less Mediocre?

If competition mainly bites by truncating the left tail \(\implies\) effect of competition should be much larger at low quantiles of the productivity distribution than at the median/right tail
We can see how the effect of competition varies across the distribution by regressing productivity quantile (within each industry/market–year) on competition IV

Problem: competition is mechanically correlated with productivity quantiles

Market Size	Sample Draw	“10th percentile”	“90th percentile”
\(n\) = 3	[-0.5, 0.2, 1.1]	-0.5 (min)	1.1 (max)
\(n\) = 6	[-1.2, -0.3, 0.1, 0.4, 0.8, 1.5]	-1.2 (min)	1.5 (2nd largest)

Key insight: “Same” quantiles are different order statistics!

Small markets: quantiles \(=\) extremes (min/max)
Large markets: quantiles \(\neq\) extremes

Bias: Larger \(n\) \(\rightarrow\) more extreme minimums \(\rightarrow\) “10th percentile” looks mechanically worse

Competition effect estimates are contaminated by sample size effects
Left tail biased downward, right tail biased upward

Solution: Add polynomial in \(n\) to purge mechanical dependence

What are your questions?

Thanks to Yiğit Sağlam for his supervision, Tim Ng for his support, and to Richard Fabling and Dave Maré pioneering work and balanced panels.

All mistakes, regrettably, are my own.

Appendix

I estimate the following for each industry \(j\)…

\[\ln y_{itj} = \beta^{(j)}_K \ln K_{itj} + \beta^{(j)}_L \ln L_{itj} + \beta^{(j)}_M \ln M_{itj} + \tau^{(j)}_t + \mu^{(j)}_i + \varepsilon_{itj}.\]

Interpretation: within industry \(j\), TFP is the firm component captured by \(\mu_i\) + residual \(\varepsilon_{itj}\)
Fixed effects: include year FE \((\tau^{(j)}_t)\) and firm FE \((\mu^{(j)}_i)\)
Industry handling: estimate separately by industry so \((\beta^{(j)}_{\cdot})\) are industry-specific; don’t compare MFP levels across industries.

What’s a demand shifter IV?

Two-stage model:

\[ \begin{align} X &= \pi Z + \Gamma W + v \quad \text{(first stage)} \\ Y &= \beta X + \delta' W + u \quad \text{(second stage)} \end{align} \]

Relevance: \(\pi \neq 0\).

Exclusion: \(Z \perp u\) and no path \(Z \to Y\) except through \(X\).

Competition estimated using market concentration & power measures

Type	Measure	Description
Structure	HHI	Weighted measure of market concentration Larger ⇒ weaker competition
Power	PCM	Percentage markup over costs Higher ⇒ weaker competition
Power	PE	How strongly cost increases reduce profits (negative values) Smaller negative ⇒ weaker competition (profits less sensitive to costs) Larger negative ⇒ stronger competition (profits more sensitive)

Herfindahl-Hirschman Index (HHI)

\[\text{HHI}_{X,jt} = \frac{\sum_{i=1}^{N_jt} X_{ijt}^2}{(\sum_{i=1}^{N_jt} X_{ijt})^2}, X \in \{Y, L\}\]

Captures how unequally market shares are distributed
Higher HHI indicates greater concentration
Lower HHI indicates more evenly distributed market share
Can be calculated using labour or output
\(\text{HHI}_{X,jt} \in (0,1]\)

Price-Cost Margin (PCM)

Average PCM \[\text{PCM}_{jt} = \frac{1}{N_{jt}}\sum_{i=1}^{N_{jt}}\max\left\{\frac{Y_{ijt} - C_{ijt}}{Y_{ijt}}, -1\right\}\]

Average profit margin across industry, giving equal weight to each firm regardless of size
Lower bound of \(-1\) to avoid small firms skewing results; i.e., \(\text{PCM}_{jt} \in [-1, 1)\)

Aggregate PCM \[\text{PCM}_{A,jt} = \frac{\sum_{i=1}^{N_{jt}}(Y_{ijt} - C_{ijt})}{\sum_{i=1}^{N_{jt}} Y_{ijt}}\]

Industry-wide profit margin, weighting each firm by its output
Ratio of total industry profits to total industry outputs
\(\text{PCM}_{A,jt} \in (-\infty, 1)\)

Profit Elasticity (PE)

\[\ln(Y_{ijt} - C_{ijt}) = \alpha_{j't} + \text{PE}_{jt} \times \frac{C_{ijt}}{Y_{ijt}} + \epsilon_{ijt}\]

Captures how responsive profits are to changes in costs
In highly competitive markets, small cost increases dramatically reduce profits
In less competitive markets, firms have more pricing power and can maintain profits despite cost increases
Negative values expected (costs reduce profits), with more negative values indicating higher competition
\(\ln(Y_{ijt} - C_{ijt}) \in (-\infty, 0]\)¹